A242161 Number of ascent sequences of length n with exactly eight flat steps.

1, 9, 90, 825, 7920, 78507, 813813, 8828820, 100321650, 1193450830, 14850852588, 193081474872, 2619543882540, 37037407198050, 545028468623100, 8336937634715580, 132393075623791785, 2180112627147691500, 37183793747600839625, 656173638174834222300

Offset

9,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 9..140

Formula

a(n) ~ Pi^(27/2) / (8! * 6^6 * sqrt(3)*exp(Pi^2/12)) * (6/Pi^2)^n * n! * sqrt(n). - Vaclav Kotesovec, Aug 27 2014

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, Expand[Sum[ If[j == i, x, 1]*b[n - 1, j, t + If[j > i, 1, 0]], {j, 0, t + 1}]]]; a[n_] := Coefficient[b[n, -1, -1], x, 8]; Table[a[n], {n, 9, 30}] (* Jean-François Alcover, Feb 10 2015, after A242153 *)

Crossrefs

Column k=8 of A242153.

Sequence in context: A186510 A158609 A229250 * A227713 A343366 A057092

Adjacent sequences: A242158 A242159 A242160 * A242162 A242163 A242164

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 05 2014

Status

approved